It seems to me that both Jacques Guy and Postal/Langendoen are
missing something important in their positions on NL cardinality.
What Guy is missing is that the idea that sentence length has no
finite bound is an interesting idealization of the behavior of
an actual device, namely, us. If one increases the quality of the
life-support systems and the strength of motivation, the maximum
attainable sentence length will increase, with no fixed limit.
Such limitations as there are on sentence length are not inherent
in the structure of the language faculty, but derive from other
features of human existence.
On the other hand, what Postal/Langendoen miss is that a sentence of
infinite length is not an idealization of our behavioral capacities:
no amount of life-support & proferred rewards are going to get an
infinite-length sentence out of anyone's mouth. The mathematics
of infinite languages might be amusing for its own sake, but it has
no bearing on the goals of generative grammar.
Avery Andrews (ada612csc.anu.edu.au)

Tom Lai <ALTOMLAICPHKVX.BITNET> writes:
"There are, for example, ideas that do not have a word in the lexicon
to express it with because the lexicon is finite."
I wouldn't think so, but I am starting to wonder if I am alone and
*nuts* in holding contrary views. To me, a finite lexicon (which I
see as the tautology of tautologies) can express new ideas and
referents, without additional words, even without new compounds, old
words simply taking on new meanings, sometimes related to the old ones,
sometimes not. As for composition, the elements seldom if ever retain
the meanings they have on their own and in other compounds. The nao3 of
dian4nao3 (Chinese for "computer") has precious little to do with the
nao3 inside our tou2, really. If some ideas, or objects, do not have
words in the lexicon to express them, it is not because the lexicon is
finite, but because not enough people have thought of that idea, or
been acquainted with that object, to press an existing word or two into
service, or make a new one up. I'm fishing there, really, because I would be
interested in learning more about those views contrary to mine.

Is Language Infinite?
It seems to me that the discussion about whether or not language is
infinite offers a textbook example of the process Alfred North
Whitehead called "extensive abstraction." Humans abstract recurrent
patterns from actual experience by vague adumbrations, then concetualize
those patterns, lose sight of their origins in extensive abstraction,
and finally reify those conceptions upon the world. The result is
what Whitehead called the "bifurcation of nature" into the world
of everyday experience and the world of science. He used this approach
to account for geometry and other kinds of formal thought. But it seem
quite applicable here. Language, as experienced on the ground, is
finite. It is constructed of a finite number of phonemes, lexemes,
grammatical constructions, etc. But we also experience the creative function of
language in the seemingly endless variety of utterances people generate.
By extensive abstraction we come to the notion that there is an infinite
possibility here, and then we formalize this adumbration as a principle
of linguistic structure. By the time we are finished, we have
the bifurcation that Whitehead so decried, language on the ground and
linguist's formal notions about what language is. The former is finite,
the latter is (for some) infinite.
Charles Laughlin
Department of Sociology & Anthropology
Carleton University
Ottawa, Ontario, CANADA K1S 5B6
charles_laughlincarleton.bitnet
Charles Laughlin <CHARLESLCARLETON.CA>

Tom Lai comments that one of the ways in which language may
meaningfully be said to be infinite is that the lexicon is open and
new words can always be introduced. Yet the entire phonological
mechanism is, meseems, concerned with maintaining adequate "distance"
between spoken symbols, and coping with bounded information content:
it is profoundly and essentially finitary. Can we not look forward to
the discovery of similar structures and results in other lexical
information? Isn't coping with finite channels and finite processing
power what language is ultimately about?
stephen p spackman